(X+12)/(x-4)=x-3

Solution for (X+12)/(x-4)=x-3 equation:

(X+12)/(X-4)=X-3

We move all terms to the left:

(X+12)/(X-4)-(X-3)=0


Domain of the equation: (X-4)!=0

We move all terms containing X to the left, all other terms to the right

X!=4

X∈R


We get rid of parentheses

(X+12)/(X-4)-X+3=0

We multiply all the terms by the denominator


(X+12)-X*(X-4)+3*(X-4)=0

We multiply parentheses

-X^2+(X+12)+4X+3X-12=0

We get rid of parentheses

-X^2+X+4X+3X+12-12=0

We add all the numbers together, and all the variables

-1X^2+8X=0

a = -1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-1)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-1}=\frac{-16}{-2}
=+8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-1}=\frac{0}{-2}
=0
$